Paper 4: Fundamentals of Business Mathematics & Statistic

6.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Rank correlation

2

2

1 6 D

N(N 1)

= −

−

∑

1 6x4 1 3

= −8(64 1) 63− = −

= 0.95

This shows there is very high positive correlation between X & Y.

Example 5 : Calculate Rank Correlation from the following data.

Marks in statistics 10 4 2 5 5 6 9 8

Marks in Maths 10 6 2 5 2 5 9 8

Solution: Table : Calculation of Rank correlation

X Y Rank R 2 D D^2

10 10 1 1 0 0

4 6 7 4 3 9

2 2 8 7.5 0.5 1

5 5 5.5 5.5 0 0

5 2 5.5 7.5 -2 4

6 5 4 5.5 -1.5 2.25

9 9 2 2 0 0

8 8 3 3 0 0

∑D 16.25^2 =

(^2) ( 13 1 ) ( (^322) )
2
D^1 m m^1 m m ...
R 1 6^1212
N(N 1)

 + − + − + 

 

= − −

∑

Here m, m 2 ... denote the number of times ranks are tied in both the variables, the subscripts & denote the

first tie, second tie,...., in both the variables

(^3 ) (^3 )

2

16.25 2 2^11 2 2

1 6^1212

8(8 1)

 + − + − 

 

= − −

16.25^66

1 6 12 12 1 6 16.25 0.5 0.5

8(63) 504

 + + 

   + + 

= − = −

1 6x17.25 1 103.5

504 504

= − = −